- Problem 1 5 Consider A State Characterized By A Real Wave Function Up To A Mul Tiplicative Constant For Simplicity Con 1 (35.64 KiB) Viewed 55 times
Problem 1.5 Consider a state characterized by a real wave function up to a mul- tiplicative constant. For simplicity consider motion in one dimension. Convince yourself that such a wave function should correspond to a bound state by con- sidering the probability current density. Show that this bound state is character- ized by vanishing momentum, i.e. (p) v = 0. Consider now the state that results from the multiplication of the above wave function by an exponential factor, i.e. x(x) = eipot/hy(x). Show that this state has momentum po. Study all the above in the momentum representation. Show that the corresponding momentum wave function (p) is translated in momentum, i.e. (p)= v(p - po).